lucid.log¶

lucid.log(a: Tensor, /) → Tensor¶

The log function computes the natural logarithm (base e) of each element in the input tensor.

Function Signature¶

def log(a: Tensor) -> Tensor

Parameters¶

a (Tensor): The input tensor for which the natural logarithm is computed.

Returns¶

Tensor:
A new tensor containing the element-wise natural logarithm of the input tensor. If a requires gradients, the resulting tensor will also require gradients.

Forward Calculation¶

The forward calculation for log is:

\[\mathbf{out}_i = \log(\mathbf{a}_i)\]

where \(\mathbf{a}_i\) is the element of the input tensor a, and \(\mathbf{out}_i\) is the corresponding element of the output tensor.

Backward Gradient Calculation¶

For a tensor a involved in the log operation, the gradient with respect to the output (out) is computed as:

\[\frac{\partial \mathbf{out}_i}{\partial \mathbf{a}_i} = \frac{1}{\mathbf{a}_i}\]

This means that for each element in the input tensor, the gradient is the reciprocal of the corresponding value in the tensor.

Example¶

>>> import lucid
>>> a = Tensor([1, 2, 3], requires_grad=True)
>>> out = lucid.log(a)
>>> print(out)
Tensor([0.         0.69314718 1.09861229], grad=None)

The log function supports tensors of arbitrary shape:

>>> import lucid
>>> a = Tensor([[1, 2], [3, 4]], requires_grad=True)
>>> out = lucid.log(a)
>>> print(out)
Tensor([[0.         0.69314718] [1.09861229 1.38629436]], grad=None)